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解答 - 几何数列

公比是：

r = 0.039000696003372186

r=0.039000696003372186

该系列的和是：

s = 211979

s=211979

此系列的通用形式是：

a_{n} = 204022 \cdot {0.039000696003372186}^{n - 1}

a_n=204022*0.039000696003372186^(n-1)

这个序列的第n项是：

204022, 7957, 310.3285380988325, 12.10302897556347, 0.472026553795956, 0.018409364130115485, 0.0007179780140540183, 2.800164226322565 E - 05, 1.0920835375032424 E - 06, 4.259201805645126 E - 08

204022,7957,310.3285380988325,12.10302897556347,0.472026553795956,0.018409364130115485,0.0007179780140540183,2.800164226322565E-05,1.0920835375032424E-06,4.259201805645126E-08

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{7957}{204022} = 0.039000696003372186$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.039000696003372186$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = 204, 022$ 、公比： $r = 0.039000696003372186$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 204022 * ((1 - {0.039000696003372186}^{2}) / (1 - 0.039000696003372186))$

$s_{2} = 204022 * ((1 - 0.0015210542887474513) / (1 - 0.039000696003372186))$

$s_{2} = 204022 * (0.9984789457112525 / (1 - 0.039000696003372186))$

$s_{2} = 204022 * (0.9984789457112525 / 0.9609993039966278)$

$s_{2} = 204022 \cdot 1.0390006960033722$

$s_{2} = 211979$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = 204, 022$ 和公比： $r = 0.039000696003372186$ 插入几何级数的公式：

$a_{n} = 204022 \cdot {0.039000696003372186}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 204022$

$a_{2} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{2 - 1} = 204022 \cdot {0.039000696003372186}^{1} = 204022 \cdot 0.039000696003372186 = 7957$

$a_{3} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{3 - 1} = 204022 \cdot {0.039000696003372186}^{2} = 204022 \cdot 0.0015210542887474513 = 310.3285380988325$

$a_{4} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{4 - 1} = 204022 \cdot {0.039000696003372186}^{3} = 204022 \cdot 5.9322175920064844 E - 05 = 12.10302897556347$

$a_{5} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{5 - 1} = 204022 \cdot {0.039000696003372186}^{4} = 204022 \cdot 2.3136061493170147 E - 06 = 0.472026553795956$

$a_{6} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{6 - 1} = 204022 \cdot {0.039000696003372186}^{5} = 204022 \cdot 9.023225010104541 E - 08 = 0.018409364130115485$

$a_{7} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{7 - 1} = 204022 \cdot {0.039000696003372186}^{6} = 204022 \cdot 3.519120555891121 E - 09 = 0.0007179780140540183$

$a_{8} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{8 - 1} = 204022 \cdot {0.039000696003372186}^{7} = 204022 \cdot 1.3724815099952775 E - 10 = 2.800164226322565 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{9 - 1} = 204022 \cdot {0.039000696003372186}^{8} = 204022 \cdot 5.352773414157504 E - 12 = 1.0920835375032424 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 204022 \cdot {0.039000696003372186}^{10 - 1} = 204022 \cdot {0.039000696003372186}^{9} = 204022 \cdot 2.0876188870048945 E - 13 = 4.259201805645126 E - 08$

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几何数列